A156327 E.g.f.: A(x) = exp( Sum_{n>=1} n*(n+3)/2 * a(n-1)*x^n/n! ) = Sum_{n>=0} a(n)*x^n/n! with a(0)=1.

1, 2, 14, 194, 4280, 134232, 5587408, 294882464, 19102334112, 1482726089600, 135370060595264, 14325189014356992, 1736329123715436544, 238698935851482530816, 36911830664814417907200

Offset

0,2

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = Sum_{k=1..n} k*(k+3)/2 * C(n-1,k-1)*a(k-1)*a(n-k) for n>0, with a(0)=1.

Example

E.g.f: A(x) = 1 + 2*x + 14*x^2/2! + 194*x^3/3! + 4280*x^4/4! + 134232*x^5/5! +...
log(A(x)) = 2*1*x + 5*2*x^2/2! + 9*14*x^3/3! + 14*194*x^4/4! + 20*4280*x^5/5! +...

Prog

(PARI) {a(n)=if(n==0, 1, n!*polcoeff(exp(sum(k=1, n, k*(k+3)/2*a(k-1)*x^k/k!)+x*O(x^n)), n))}
(PARI) {a(n)=if(n==0, 1, sum(k=1, n, k*(k+3)/2*binomial(n-1, k-1)*a(k-1)*a(n-k)))}

Crossrefs

Cf. A156325, A156326.

Sequence in context: A158102 A067902 A132611 * A047796 A305112 A336949

Adjacent sequences: A156324 A156325 A156326 * A156328 A156329 A156330

Keyword

nonn

Author

Paul D. Hanna, Feb 08 2009

Status

approved